In the 20th minute the visitors took the lead as Francesco Lodi's free kick from out wide on the right squirmed under the body of Leali and ended up in the back of the net.
Frosinone gradually fought their way into the match and on the stroke of half time Matteo Ciofani placed an attempt inches wide of the post.
Moments later Leali was forced to turn behind a strike from Di Natale, before the veteran curled another free kick inches wide of the target.
Nicolas Castillo then wasted another promising opening for the visitors when he was slipped into the box and dragged a strike across the keeper and beyond the far post.
As the game moved into stoppage time, Lodi wasted the chance to make the game safe when his effort was saved by Leali, but his side were not made to pay as they held on to claim the win.